CBSE Class 10 Math Question Paper 2016 | Q9

The given question is a medium difficulty 2-mark question from the chapter Arithmetic Progressions. Concept tested: Applying the formula to compute the nth term of an arithmetic progression. The question appeared in Section B of the 2016 CBSE class 10 board paper.

Question 9: The 4^th term of an A.P. is zero. Prove that the 25^th term of the A.P. is three times its 11^th term

Video Explanation

Explanatory Answer | CBSE 2016 Maths Paper Q9

The n^th term of AP, a_n = a₁ + (n - 1) d
where a₁ is the first term and d is the common difference

Given Data: a₄ = 0
i.e., a₄ = a₁ + (4 - 1) d = 0
or a₁ + 3d = 0
or a₁ = -3d ..... (1)

To Prove: a₂₅ = 3(a₁₁)

a₂₅ = a₁ + (25 - 1 ) d = a₁ + 24d ..... (2)
Substitute a₁ = -3d in eqn (2)
a₂₅ = -3d + 24d = 21d ..... (3)

a₁₁ = a₁ + (11 - 1) d = a₁ + 10d ..... (4)
Substitute a₁ = -3d in eqn (4)
a₁₁ = -3d + 10d = 7d ..... (5)

Compare equations (3) and (5)
Equation (3): a₂₅ = 21d
Equation (5): a₁₁ = 7d
21d = 3 × 7d
Or a₂₅ = 3 × a₁₁